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Estimation with multivariate outcomes having nonignorable item nonresponse

Abstract

To estimate unknown population parameters based on \({\varvec{y}}\), a vector of multivariate outcomes having nonignorable item nonresponse that directly depends on \({\varvec{y}}\), we propose an innovative inverse propensity weighting approach when the joint distribution of \({\varvec{y}}\) and associated covariate \({\varvec{x}}\) is nonparametric and the nonresponse probability conditional on \({\varvec{y}}\) and \({\varvec{x}}\) has a parametric form. To deal with the identifiability issue, we utilize a nonresponse instrument \({\varvec{z}}\), an auxiliary variable related to \({\varvec{y}}\) but not related to the nonresponse probability conditional on \({\varvec{y}}\) and \({\varvec{x}}\). We utilize a modified generalized method of moments to obtain estimators of the parameters in the nonresponse probability. Simulation results are presented and an application is illustrated in a real data set.

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Acknowledgements

We are grateful to the associate editor and two referees for comments and suggestions that led to improvements of the paper. Lyu Ni’s research was supported by the Shanghai Sailing Program 22YF1411300. Jun Shao’s research was supported by the National Natural Science Foundation of China Grant 11831008 and the U.S. National Science Foundation Grant DMS-1914411.

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Correspondence to Jun Shao.

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Ni, L., Shao, J. Estimation with multivariate outcomes having nonignorable item nonresponse. Ann Inst Stat Math (2022). https://doi.org/10.1007/s10463-022-00836-4

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  • DOI: https://doi.org/10.1007/s10463-022-00836-4

Keywords

  • Generalized method of moments
  • Item nonresponse
  • Inverse propensity weighting
  • Multivariate outcome
  • Nonresponse instrument